Question

The market consensus is that Analog Electronic Corporation has an ROE = 13%, a beta of 2.00, and plans to maintain indefinitely its traditional plowback ratio of 3/5. This year’s earnings were $3.40 per share. The annual dividend was just paid. The consensus estimate of the coming year’s market return is 11%, and T-bills currently offer a 5% return.

a. Find the price at which Analog stock should sell. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Price?

b. Calculate the P/E ratio. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Leading?

Trailing?

c. Calculate the present value of growth opportunities. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 2 decimal places.)

PVGO?

d. Suppose your research convinces you Analog will announce momentarily that it will immediately change its plowback ratio to 2/5. Find the intrinsic value of the stock. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Intrinsic Value?

Answer 1

a. We know T bills are risk free, so Return on T bills = Risk free rate = 5%

According to CAPM

Required rate of return on stock = Risk free rate + Beta(market return - risk free rate) = 5% + 2(11% - 5%) = 5% + 2 x 6% = 5% + 12% = 17%

Sustainable Growth rate = g = ROE x plowback ratio = 13% x (3/5) = 7.8%

Dividend payout ratio = 1-plowback ratio = 1- (3/5) = 2/5

Next year EPS = E1 = Current EPS (1+g) = 3.40(1+7.8%) = 3.40 x 1.078 = 3.6652

Next year dividend = D1 = Next year EPS x dividend payout ratio = 3.6652 x (2/5) = 1.4660

According constant growth rate model

Current price of stock = D1 / (r - g) = 1.4660 / (17% - 7.8%)= 1.4660 / 9.20% = 15.9347 = $15.93 (rounded to two decimal places)

Hence Price for which stock should sell = $15.93

b. Leading P/E = Current Price / E1 = 15.9347 / 3.6652 = 4.3475 = 4.35 (rounded to two decimal places)

Leading P/E = 4.35

Trailing P/E = Current Price / Current EPS = 15.9347 / 3.40 = 4.6866 = 4.69 (rounded to two decimal places)

Trailing P/E = 4.69

c. We know that

Current Price = (E1 / r) + PVGO

15.9347 = (3.40 / 17%) + PVGO

15.9347 = 20 + PVGO

PVGO = 15.9347 - 20 = -4.0653 = - $4.07 (rounded to two decimal places)

Hence PVGO = -$4.07

d. Since plowback has changed to 2/5

Sustainable Growth rate = g = ROE x plowback ratio = 13% x (2/5) = 5.2%

Dividend payout ratio = 1-plowback ratio = 1- (2/5) = 3/5

Next year EPS = E1 = Current EPS (1+g) = 3.40(1+5.2%) = 3.40 x 1.052 = 3.5768

Next year dividend = D1 = Next year EPS x dividend payout ratio = 3.5768 x (3/5) = 2.1460

According constant growth rate model

Current price of stock = D1 / (r - g) = 2.1460 / (17% - 5.2%)= 2.1460 / 11.8% = 18.1864 = $18.19 (rounded to two decimal places)

Hence Intrinsic value of stock = Current price of stock = $18.19